Abstract
We consider a pseudodifferential operator P whose symbol has an asymptotic expansion by quasi homogeneous symbols and the principal symbol is degenerate on a submanifold. Under appropriate conditions, P has the discrete spectrum. Then we can get the asymptotic behavior of the counting function of eigenvalues of P with remainder estimate according to various cases. 0. Introduction. We consider the asymptotic behavior of eigenvalues for a class of pseudodifferential operators on Rn containing the Schrόdinger operator with magnetic field: (0.1) pw(x,D) = H(a) + V{x)
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